In the early 1980’s, a few articles were published in the Choctaw Nation of Oklahoma’s Bishinik that suggested the Choctaw of ancient times divided their calendar into two seasons. Writer Len Green discussed the timing of the seasons as well as the need for an intercalary time, as is necessary with lunisolarcalendars.
The year was divided in two parts as indicated, with Tek i Hvshi beginning around the time of the vernal equinox (about March 22) and Chvfiskono beginning around the autumnal equinox (September 22).
…to keep the months in harmony with the ripening of fruits and other seasonal events, every two or three years an additional month, Luak Mosholi (extinguishing fire) was observed to take up the slack. It is not known at this time when that month occurred, or whether it was in the summer or winter, but that’s the way they used to do it.
Full articles are transcribed here. Another seasonal question then: When was the Choctaw new year? A more important question, because it may be hard to ever answer the previous one: who knows the sources from where each of the above suggestions may have been derived?